Results 11 to 20 of about 2,009 (123)

Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate [PDF]

, 2004
Consider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N 2 V (N(xi − xj)), where x = (x1, . . ., xN) denotes the positions of the particles. Let HN denote the Hamiltonian of the system and let ψN,t be the
L. Erdős, B. Schlein, H. Yau
semanticscholar   +1 more source

E8 spectral curves

Proceedings of the London Mathematical Society, Volume 121, Issue 4, Page 954-1032, October 2020., 2020
Abstract I provide an explicit construction of spectral curves for the affine E8 relativistic Toda chain. Their closed‐form expression is obtained by determining the full set of character relations in the representation ring of E8 for the exterior algebra of the adjoint representation; this is in turn employed to provide an explicit construction of ...
Andrea Brini
wiley   +1 more source

Solitons for the coupled matrix nonlinear Schrödinger-type equations and the related Schrödinger flow

Open Mathematics, 2023
In this article, the coupled matrix nonlinear Schrödinger (NLS) type equations are gauge equivalent to the equation of Schrödinger flow from R1{{\mathbb{R}}}^{1} to complex Grassmannian manifold G˜n,k=GL(n,C)∕GL(k,C)×GL(n−k,C),{\widetilde{G}}_{n,k}={\rm ...
Zhong Shiping, Zhao Zehui, Wan Xinjie
doaj   +1 more source

Intertwining semiclassical solutions to a Schrödinger-Newton system [PDF]

, 2011
We study the problem ( (−"i∇ + A(x)) 2 u + V (x)u = " 2 1 |x| ∗ |u| 2 u, u ∈ L 2 (R 3 ,C), "∇u + iAu ∈ L 2 (R 3 ,C 3 ), where A: R3 → R3 is an exterior magnetic potential, V : R3 → R is an exte- rior electric potential, and " is a small positive ...
S. Cingolani, M. Clapp, S. Secchi
semanticscholar   +1 more source

Existence of normalized solutions for the coupled elliptic system with quadratic nonlinearity

Advanced Nonlinear Studies, 2022
In the present paper, we study the existence of the normalized solutions for the following coupled elliptic system with quadratic nonlinearity −Δu−λ1u=μ1∣u∣u+βuvinRN,−Δv−λ2v=μ2∣v∣v+β2u2inRN,\left\{\begin{array}{ll}-\Delta u-{\lambda }_{1}u={\mu }_{1}| u|
Wang Jun, Wang Xuan, Wei Song
doaj   +1 more source

Infinitely many solutions for quasilinear Schrödinger equations with sign-changing nonlinearity without the aid of 4-superlinear at infinity

Demonstratio Mathematica, 2022
In this article, we will prove the existence of infinitely many solutions for a class of quasilinear Schrödinger equations without assuming the 4-superlinear at infinity on the nonlinearity. We achieve our goal by using the Fountain theorem.
Khiddi Mustapha, Essafi Lakbir
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GLOBAL WELL-POSEDNESS OF THE PERIODIC CUBIC FOURTH ORDER NLS IN NEGATIVE SOBOLEV SPACES

Forum of Mathematics, Sigma, 2018
We consider the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation (4NLS) on the circle. In particular, we prove global well-posedness of the renormalized 4NLS in negative Sobolev spaces $H^{s}(\mathbb{T})$
TADAHIRO OH, YUZHAO WANG
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Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction

Advances in Nonlinear Analysis, 2021
In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region
Wang Jun
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Optical vortices in dispersive nonlinear Kerr‐type media

International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 18, Page 949-967, 2004., 2004
The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be ...
Lubomir M. Kovachev
wiley   +1 more source

The homogeneous balance of undetermined coefficients method and its application

Open Mathematics, 2016
The homogeneous balance of undetermined coefficients method is firstly proposed to solve such nonlinear partial differential equations (PDEs), the balance numbers of which are not positive integers.
Wei Yi, He Xin-Dang, Yang Xiao-Feng
doaj   +1 more source